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Surface defects in the $O(N)$ model
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abstract
I study the two-dimensional defects of the $d$ dimensional critical $O(N)$ model and the defect RG flows between them. By combining the $\epsilon$-expansion around $d = 4$ and $d = 6$ as well as large $N$ techniques, I find new conformal defects and examine their behavior across dimensions and at various $N$. I discuss how some of these fixed points relate to the known ordinary, special and extraordinary transitions in the 3d theory, as well as examine the presence of new symmetry breaking fixed points preserving an $O(p) \times O(N-p)$ subgroup of $O(N)$ for $N \le N_c$ (with the estimate $N_c = 6$). I characterise these fixed points by obtaining their conformal anomaly coefficients, their 1-point functions and comment on the calculation of their string potential. These results establish surface operators as a viable approach to the characterisation of interface critical phenomena in the 3d critical $O(N)$ model.
Forward citations
Cited by 7 Pith papers
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Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter
In a strictly short-range XY model made of a plane intersected by parallel planes, true long-range order appears along the intersection lines when the parallel planes enter a Berezinskii-Kosterlitz-Thouless critical phase.
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Transdimensional Defects
Defects of continuously adjustable dimension p=2+δ are defined and analyzed in the O(N) model, yielding new interfaces and non-local 3d CFTs.
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Rank matching in renormalization-group irreversibility: Exact defect and entropic tests
A counting rule ("rank matching") separates RG endpoint inequalities from running monotonicity, with exact defect b-function transitions and an F-loss profile reversal.
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Ising surface defects can get dirty
Replica one-loop RG of Wilson-Fisher theory with surface random field yields a mixed-stable dirty defect fixed point and logarithmic multiplets in the N o0 limit.
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Surprises in the Ordinary: $O(N)$ Invariant Surface Defect in the $\epsilon$-expansion
The authors compute defect CFT data to third order in the epsilon expansion and discover approximate 'shadow' relations between surface and bulk scaling dimensions.
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Defect Conformal Manifolds from Phantom (Non-Invertible) Symmetries
Continuous non-invertible 'phantom' symmetries of the folded theory generate defect conformal manifolds in (1+1)d CFTs and control how the reflection coefficient changes along the manifold.
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Chiral algebra correlators of the $6$d, $\mathcal{N}=(2,0)$ theory with a defect
A chiral-algebra bootstrap reproduces the defect two-point correlators of the 6d (2,0) theory using only bulk-channel data and predicts new defect-channel OPE coefficients.
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